On a result of nilpotent subgroups of solvable groups

Document Type : Research Paper

Author

Department of Mathematics, Texas State University, 601 University Drive, San Marcos, TX 78666, USA

Abstract

‎Heineken [‎H‎. ‎Heineken‎, ‎Nilpotent subgroups of finite soluble groups‎, Arch‎. ‎Math.(Basel)‎, ‎ 56 no‎. ‎5 (1991) 417--423‎.] studied the order of the nilpotent subgroups of the largest order of a solvable group‎. ‎We point out an error‎, ‎and thus refute the proof of the main result of [‎H‎. ‎Heineken‎, ‎Nilpotent subgroups of finite soluble groups‎, Arch‎. ‎Math.(Basel)}‎, 56 no‎. ‎5 (1991) 417--423‎].

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References

[1] J. Cossey, Z. Halasi, A. Maróti and H. N. Nguyen, On a conjecture of Gluck, Math. Z.,279 no. 3-4 (2015) 1067–1080.
[2] H. Heineken, Nilpotent subgroups of finite soluble groups, Arch. Math.(Basel), 56 no. 5 (1991) 417–423.
[3] M. Liebeck and L. Pyber, Upper bounds for the number of conjugacy classes of a finite group, J. Algebra, 198 no.
2 (1997) 538–562.
[4] L. Pyber, How abelian is a finite group? The mathematics of Paul Erdös, I, Algorithms Combin., 13, Springer,
Berlin, 1997 372–384.
International Journal of Group Theory
Volume 11, Issue 3 - Serial Number 3
September 2022
Pages 187-189

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History

  • Receive Date: 02 May 2021
  • Revise Date: 22 September 2021
  • Accept Date: 24 September 2021
  • Published Online: 01 September 2022

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